Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

Deep learning for RNA structure prediction

Predicting RNA structures from sequences with computational approaches is of vital importance in RNA biology considering the high costs of experimental determination. AI methods have revolutionized this field in recent years, enabling RNA structure prediction with increasingly higher accuracy and efficiency. With an increase in the number of models proposed for this task, this review presents a timely summary of the applications of AI, particularly deep learning, in RNA structure prediction, highlighting their methodology advances as well as the challenges and opportunities for further work in this field.

rCGMM: A Coarse-Grained Force Field Embedding Elastic Network for Studying Small Noncoding RNA Dynamics

Short noncoding RNA molecules play significant roles in catalysis, biological regulation, and disease pathways. Their assessment through sequence-based approaches has been a challenge, compounded by the significant structural flexibility accrued from six free backbone torsions per nucleotide. To efficiently study the structure and dynamics of an extensive repertoire of these molecules in a high throughput mode, we have built a coarse-grained force field using one, two, three, and four pseudoatoms to represent the phosphate, sugar, pyrimidines, and purines, respectively. The Boltzmann inversion method was applied to structures of 5 piRNA, 8 miRNA, and 13 siRNA from the Nucleic Acid Database (NDB) to estimate the initial force field parameters and iteratively optimized through 1 μs molecular dynamics run by comparing against an equivalent all-atom simulation using the CHARMM36 force field. We applied an elastic net to model the hydrogen bond network stabilizing the local structure for double-stranded cases. A spine using pseudoatoms was calculated for the same from the coarse-grain beads, and all beads within a threshold radial distance were constrained using soft distance potentials. Lennard-Jones and Coulomb's potential function modeled the nonbonded interaction. Benchmarks on 26 molecules compared through root-mean-square deviation graphs against all-atom simulation show close concurrence for single- and double-stranded small noncoding RNA molecules. The rCGMM force field is available for download at https://github.com/majumderS/rCGMM.

Driving Forces of RNA Condensation Revealed through Coarse-Grained Modeling with Explicit Mg2

RNAs are major drivers of phase separation in the formation of biomolecular condensates, and can undergo protein-free phase separation in the presence of divalent ions or crowding agents. Much remains to be understood regarding how the complex interplay of base stacking, base pairing, electrostatics, ion interactions, and particularly structural propensities governs RNA phase behavior. Here we develop an intermediate resolution model for condensates of RNAs (iConRNA) that can capture key local and long-range structure features of dynamic RNAs and simulate their spontaneous phase transitions with Mg2+. Representing each nucleotide using 6-7 beads, iConRNA accurately captures base stacking and pairing and includes explicit Mg2+. The model does not only reproduce major conformational properties of poly(rA) and poly(rU), but also correctly folds small structured RNAs and predicts their melting temperatures. With an effective model of explicit Mg2+, iConRNA successfully recapitulates experimentally observed lower critical solution temperature phase separation of poly(rA) and triplet repeats, and critically, the nontrivial dependence of phase transitions on RNA sequence, length, concentration, and Mg2+ level. Further mechanistic analysis reveals a key role of RNA folding in modulating phase separation as well as its temperature and ion dependence, besides other driving forces such as Mg2+-phosphate interactions, base stacking, and base pairing. These studies also support iConRNA as a powerful tool for direct simulation of RNA-driven phase transitions, enabling molecular studies of how RNA conformational dynamics and its response to complex condensate environment control the phase behavior and condensate material properties.

SIGNIFICANCE STATEMENT

Dynamic RNAs and proteins are major drivers of biomolecular phase separation that has been recently discovered to underlie numerous biological processes and be involved in many human diseases. Molecular simulation has an indispensable role to play in dissecting the driving forces and regulation of biomolecular phase separation. The current work describes a high-resolution coarse-grained RNA model that is capable of describing the structure dynamics and complex sequence, concentration, temperature and ion dependent phase transitions of flexible RNAs. The study further reveals a central role of RNA folding in coordinating Mg2+-phosphate interactions, base stacking, and base pairing to drive phase separation, paving the road for studies of RNA-mediated phase separation in relevant biological contexts.

Advances in the field of RNA 3D structure prediction and modeling, with purely theoretical approaches, and with the use of experimental data

Recent advancements in RNA three-dimensional (3D) structure prediction have provided significant insights into RNA biology, highlighting the essential role of RNA in cellular functions and its therapeutic potential. This review summarizes the latest developments in computational methods, particularly the incorporation of artificial intelligence and machine learning, which have improved the efficiency and accuracy of RNA structure predictions. We also discuss the integration of new experimental data types, including cryoelectron microscopy (cryo-EM) techniques and high-throughput sequencing, which have transformed RNA structure modeling. The combination of experimental advances with computational methods represents a significant leap in RNA structure determination. We review the outcomes of RNA-Puzzles and critical assessment of structure prediction (CASP) challenges, which assess the state of the field and limitations of existing methods. Future perspectives are discussed, focusing on the impact of RNA 3D structure prediction on understanding RNA mechanisms and its implications for drug discovery and RNA-targeted therapies, opening new avenues in molecular biology.

3dDNAscoreA: A scoring function for evaluation of DNA 3D structures

DNA molecules are vital macromolecules that play a fundamental role in many cellular processes and have broad applications in medicine. For example, DNA aptamers have been rapidly developed for diagnosis, biosensors, and clinical therapy. Recently, we proposed a computational method of predicting DNA 3D structures, called 3dDNA. However, it lacks a scoring function to evaluate the predicted DNA 3D structures, and so they are not ranked for users. Here, we report a scoring function, 3dDNAscoreA, for evaluation of DNA 3D structures based on a deep learning model ARES for RNA 3D structure evaluation but using a new strategy for training. 3dDNAscoreA is benchmarked on two test sets to show its ability to rank DNA 3D structures and select the native and near-native structures.

3dRNA/DNA: 3D Structure Prediction from RNA to DNA

There is an increasing need for determining 3D structures of DNAs, e.g., for increasing the efficiency of DNA aptamer selection. Recently, we have proposed a computational method of 3D structure prediction of DNAs, called 3dDNA, which has been integrated into our original web server 3dRNA, now renamed 3dRNA/DNA (http://biophy.hust.edu.cn/new/3dRNA). Currently, 3dDNA can only output the predicted DNA 3D structures for users but cannot rank them as an energy function for assessing DNA 3D structures is still lacking. Here, we first provide a brief introduction to 3dDNA and then introduce a new energy function, 3dDNAscore, for the assessment of DNA 3D structures. 3dDNAscore is an all-atom knowledge-based potential by integrating 86 atomic types from nucleic acids. Benchmarks demonstrate that 3dDNAscore can effectively identify near-native structures from the decoys generated by 3dDNA, thus enhancing the completeness of 3dDNA.

Accurate and Efficient SAXS/SANS Implementation Including Solvation Layer Effects Suitable for Molecular Simulations

Small-angle X-ray and neutron scattering (SAXS/SANS) provide valuable insights into the structure and dynamics of biomolecules in solution, complementing a wide range of structural techniques, including molecular dynamics simulations. As contrast-based methods, they are sensitive not only to structural properties but also to solvent-solute interactions. Their use in molecular dynamics simulations requires a forward model that should be as fast and accurate as possible. In this work, we demonstrate the feasibility of calculating SAXS and SANS intensities using a coarse-grained representation consisting of one bead per amino acid and three beads per nucleic acid, with form factors that can be corrected on the fly to account for solvation effects at no additional computational cost. By coupling this forward model with molecular dynamics simulations restrained with SAS data, it is possible to determine conformational ensembles or refine the structure and dynamics of proteins and nucleic acids in agreement with the experimental results. To assess the robustness of this approach, we applied it to gelsolin, for which we acquired SAXS data on its closed state, and to a UP1-microRNA complex, for which we used previously collected measurements. Our hybrid-resolution small-angle scattering (hySAS) implementation, being distributed in PLUMED, can be used with atomistic and coarse-grained simulations using diverse restraining strategies.

RIBFIND2: Identifying rigid bodies in protein and nucleic acid structures

Molecular structures are often fitted into cryo-EM maps by flexible fitting. When this requires large conformational changes, identifying rigid bodies can help optimize the model-map fit. Tools for identifying rigid bodies in protein structures exist, however an equivalent for nucleic acid structures is lacking. With the increase in cryo-EM maps containing RNA and progress in RNA structure prediction, there is a need for such tools. We previously developed RIBFIND, a program for clustering protein secondary structures into rigid bodies. In RIBFIND2, this approach is extended to nucleic acid structures. RIBFIND2 can identify biologically relevant rigid bodies in important groups of complex RNA structures, capturing a wide range of dynamics, including large rigid-body movements. The usefulness of RIBFIND2-assigned rigid bodies in cryo-EM model refinement was demonstrated on three examples, with two conformations each: Group II Intron complexed IEP, Internal Ribosome Entry Site and the Processome, using cryo-EM maps at 2.7-5 Å resolution. A hierarchical refinement approach, performed on progressively smaller sets of RIBFIND2 rigid bodies, was clearly shown to have an advantage over classical all-atom refinement. RIBFIND2 is available via a web server with structure visualization and as a standalone tool.

RNA 3D Structure Prediction: Progress and Perspective

Ribonucleic acid (RNA) molecules play vital roles in numerous important biological functions such as catalysis and gene regulation. The functions of RNAs are strongly coupled to their structures or proper structure changes, and RNA structure prediction has been paid much attention in the last two decades. Some computational models have been developed to predict RNA three-dimensional (3D) structures in silico, and these models are generally composed of predicting RNA 3D structure ensemble, evaluating near-native RNAs from the structure ensemble, and refining the identified RNAs. In this review, we will make a comprehensive overview of the recent advances in RNA 3D structure modeling, including structure ensemble prediction, evaluation, and refinement. Finally, we will emphasize some insights and perspectives in modeling RNA 3D structures.

RNAJP: enhanced RNA 3D structure predictions with non-canonical interactions and global topology sampling

RNA 3D structures are critical for understanding their functions. However, only a limited number of RNA structures have been experimentally solved, so computational prediction methods are highly desirable. Nevertheless, accurate prediction of RNA 3D structures, especially those containing multiway junctions, remains a significant challenge, mainly due to the complicated non-canonical base pairing and stacking interactions in the junction loops and the possible long-range interactions between loop structures. Here we present RNAJP ('RNA Junction Prediction'), a nucleotide- and helix-level coarse-grained model for the prediction of RNA 3D structures, particularly junction structures, from a given 2D structure. Through global sampling of the 3D arrangements of the helices in junctions using molecular dynamics simulations and in explicit consideration of non-canonical base pairing and base stacking interactions as well as long-range loop-loop interactions, the model can provide significantly improved predictions for multibranched junction structures than existing methods. Moreover, integrated with additional restraints from experiments, such as junction topology and long-range interactions, the model may serve as a useful structure generator for various applications.

cgRNASP: coarse-grained statistical potentials with residue separation for RNA structure evaluation

Knowledge-based statistical potentials are very important for RNA 3-dimensional (3D) structure prediction and evaluation. In recent years, various coarse-grained (CG) and all-atom models have been developed for predicting RNA 3D structures, while there is still lack of reliable CG statistical potentials not only for CG structure evaluation but also for all-atom structure evaluation at high efficiency. In this work, we have developed a series of residue-separation-based CG statistical potentials at different CG levels for RNA 3D structure evaluation, namely cgRNASP, which is composed of long-ranged and short-ranged interactions by residue separation. Compared with the newly developed all-atom rsRNASP, the short-ranged interaction in cgRNASP was involved more subtly and completely. Our examinations show that, the performance of cgRNASP varies with CG levels and compared with rsRNASP, cgRNASP has similarly good performance for extensive types of test datasets and can have slightly better performance for the realistic dataset-RNA-Puzzles dataset. Furthermore, cgRNASP is strikingly more efficient than all-atom statistical potentials/scoring functions, and can be apparently superior to other all-atom statistical potentials and scoring functions trained from neural networks for the RNA-Puzzles dataset. cgRNASP is available at https://github.com/Tan-group/cgRNASP.

RNAStat: An Integrated Tool for Statistical Analysis of RNA 3D Structures

The 3D architectures of RNAs are essential for understanding their cellular functions. While an accurate scoring function based on the statistics of known RNA structures is a key component for successful RNA structure prediction or evaluation, there are few tools or web servers that can be directly used to make comprehensive statistical analysis for RNA 3D structures. In this work, we developed RNAStat, an integrated tool for making statistics on RNA 3D structures. For given RNA structures, RNAStat automatically calculates RNA structural properties such as size and shape, and shows their distributions. Based on the RNA structure annotation from DSSR, RNAStat provides statistical information of RNA secondary structure motifs including canonical/non-canonical base pairs, stems, and various loops. In particular, the geometry of base-pairing/stacking can be calculated in RNAStat by constructing a local coordinate system for each base. In addition, RNAStat also supplies the distribution of distance between any atoms to the users to help build distance-based RNA statistical potentials. To test the usability of the tool, we established a non-redundant RNA 3D structure dataset, and based on the dataset, we made a comprehensive statistical analysis on RNA structures, which could have the guiding significance for RNA structure modeling. The python code of RNAStat, the dataset used in this work, and corresponding statistical data files are freely available at GitHub (https://github.com/RNA-folding-lab/RNAStat).

rsRNASP: A residue-separation-based statistical potential for RNA 3D structure evaluation

Knowledge-based statistical potentials have been shown to be rather effective in protein 3-dimensional (3D) structure evaluation and prediction. Recently, several statistical potentials have been developed for RNA 3D structure evaluation, while their performances are either still at a low level for the test datasets from structure prediction models or dependent on the "black-box" process through neural networks. In this work, we have developed an all-atom distance-dependent statistical potential based on residue separation for RNA 3D structure evaluation, namely rsRNASP, which is composed of short- and long-ranged potentials distinguished by residue separation. The extensive examinations against available RNA test datasets show that rsRNASP has apparently higher performance than the existing statistical potentials for the realistic test datasets with large RNAs from structure prediction models, including the newly released RNA-Puzzles dataset, and is comparable to the existing top statistical potentials for the test datasets with small RNAs or near-native decoys. In addition, rsRNASP is superior to RNA3DCNN, a recently developed scoring function through 3D convolutional neural networks. rsRNASP and the relevant databases are available to the public.

A complete Fourier-synthesis-based backbone-conformation-dependent library for proteins

While broadening the applicability of (φ/ψ)-dependent target values for the bond angles in the peptide backbone, sequence/conformation categories with too few residues to analyze via previous methods were encountered. Here, a method of describing a conformation-dependent library (CDL) using two-dimensional Fourier coefficients is reported where the number of coefficients for individual categories is determined via complete cross-validation. Sample sizes are increased further by selective blending of categories with similar patterns of conformational dependence. An additional advantage of the Fourier-synthesis-based CDL is that it uses continuous functions and has no artifactual steps near the edges of populated regions of φ/ψ space. A set of libraries for the seven main-chain bond angles, along with the ω and ζ angles, was created based on a set of Fourier analyses of 48 368 residues selected from high-resolution models in the wwPDB. This new library encompasses both trans- and cis-peptide bonds and outperforms currently used discrete CDLs.

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

RNA-Puzzles toolkit: a computational resource of RNA 3D structure benchmark datasets, structure manipulation, and evaluation tools

Significant improvements have been made in the efficiency and accuracy of RNA 3D structure prediction methods during the succeeding challenges of RNA-Puzzles, a community-wide effort on the assessment of blind prediction of RNA tertiary structures. The RNA-Puzzles contest has shown, among others, that the development and validation of computational methods for RNA fold prediction strongly depend on the benchmark datasets and the structure comparison algorithms. Yet, there has been no systematic benchmark set or decoy structures available for the 3D structure prediction of RNA, hindering the standardization of comparative tests in the modeling of RNA structure. Furthermore, there has not been a unified set of tools that allows deep and complete RNA structure analysis, and at the same time, that is easy to use. Here, we present RNA-Puzzles toolkit, a computational resource including (i) decoy sets generated by different RNA 3D structure prediction methods (raw, for-evaluation and standardized datasets), (ii) 3D structure normalization, analysis, manipulation, visualization tools (RNA_format, RNA_normalizer, rna-tools) and (iii) 3D structure comparison metric tools (RNAQUA, MCQ4Structures). This resource provides a full list of computational tools as well as a standard RNA 3D structure prediction assessment protocol for the community.

All-Atom Knowledge-Based Potential for RNA Structure Discrimination Based on the Distance-Scaled Finite Ideal-Gas Reference State

Noncoding RNAs are increasingly found to play a wide variety of roles in living organisms. Yet, their functional mechanisms are poorly understood because their structures are difficult to determine experimentally. As a result, developing more effective computational techniques to predict RNA structures becomes increasingly an urgent task. One key challenge in RNA structure prediction is the lack of an accurate free energy function to guide RNA folding and discriminate native and near-native structures from decoy conformations. In this study, we developed an all-atom distance-dependent knowledge-based energy function for RNA that is based on a reference state (distance-scaled finite ideal-gas reference state, DFIRE) proven successful for protein structure discrimination. Using four separate benchmarks including RNA puzzles, we found that this DFIRE-based RNA statistical energy function is able to discriminate native and near-native structures against decoys with performance comparable with or better than several existing scoring functions compared. The energy function is expected to be useful for improving the detection of RNA near-native structures.

Sequence-dependent RNA helix conformational preferences predictably impact tertiary structure formation

Structured RNAs and RNA complexes underlie biological processes ranging from control of gene expression to protein translation. Approximately 50% of nucleotides within known structured RNAs are folded into Watson-Crick (WC) base pairs, and sequence changes that preserve these pairs are typically assumed to preserve higher-order RNA structure and binding of macromolecule partners. Here, we report that indirect effects of the helix sequence on RNA tertiary stability are, in fact, significant but are nevertheless predictable from a simple computational model called RNAMake-∆∆G. When tested through the RNA on a massively parallel array (RNA-MaP) experimental platform, blind predictions for >1500 variants of the tectoRNA heterodimer model system achieve high accuracy (rmsd 0.34 and 0.77 kcal/mol for sequence and length changes, respectively). Detailed comparison of predictions to experiments support a microscopic picture of how helix sequence changes subtly modulate conformational fluctuations at each base-pair step, which accumulate to impact RNA tertiary structure stability. Our study reveals a previously overlooked phenomenon in RNA structure formation and provides a framework of computation and experiment for understanding helix conformational preferences and their impact across biological RNA and RNA-protein assemblies.

Determination of an effective scoring function for RNA-RNA interactions with a physics-based double-iterative method

RNA–RNA interactions play fundamental roles in gene and cell regulation. Therefore, accurate prediction of RNA–RNA interactions is critical to determine their complex structures and understand the molecular mechanism of the interactions. Here, we have developed a physics-based double-iterative strategy to determine the effective potentials for RNA–RNA interactions based on a training set of 97 diverse RNA–RNA complexes. The double-iterative strategy circumvented the reference state problem in knowledge-based scoring functions by updating the potentials through iteration and also overcame the decoy-dependent limitation in previous iterative methods by constructing the decoys iteratively. The derived scoring function, which is referred to as DITScoreRR, was evaluated on an RNA–RNA docking benchmark of 60 test cases and compared with three other scoring functions. It was shown that for bound docking, our scoring function DITScoreRR obtained the excellent success rates of 90% and 98.3% in binding mode predictions when the top 1 and 10 predictions were considered, compared to 63.3% and 71.7% for van der Waals interactions, 45.0% and 65.0% for ITScorePP, and 11.7% and 26.7% for ZDOCK 2.1, respectively. For unbound docking, DITScoreRR achieved the good success rates of 53.3% and 71.7% in binding mode predictions when the top 1 and 10 predictions were considered, compared to 13.3% and 28.3% for van der Waals interactions, 11.7% and 26.7% for our ITScorePP, and 3.3% and 6.7% for ZDOCK 2.1, respectively. DITScoreRR also performed significantly better in ranking decoys and obtained significantly higher score-RMSD correlations than the other three scoring functions. DITScoreRR will be of great value for the prediction and design of RNA structures and RNA–RNA complexes.

What is the best reference state for building statistical potentials in RNA 3D structure evaluation?

Knowledge-based statistical potentials have been shown to be efficient in protein structure evaluation/prediction, and the core difference between various statistical potentials is attributed to the choice of reference states. However, for RNA 3D structure evaluation, a comprehensive examination on reference states is still lacking. In this work, we built six statistical potentials based on six reference states widely used in protein structure evaluation, including averaging, quasi-chemical approximation, atom-shuffled, finite-ideal-gas, spherical-noninteracting, and random-walk-chain reference states, and we examined the six reference states against three RNA test sets including six subsets. Our extensive examinations show that, overall, for identifying native structures and ranking decoy structures, the finite-ideal-gas and random-walk-chain reference states are slightly superior to others, while for identifying near-native structures, there is only a slight difference between these reference states. Our further analyses show that the performance of a statistical potential is apparently dependent on the quality of the training set. Furthermore, we found that the performance of a statistical potential is closely related to the origin of test sets, and for the three realistic test subsets, the six statistical potentials have overall unsatisfactory performance. This work presents a comprehensive examination on the existing reference states and statistical potentials for RNA 3D structure evaluation.

Effects of Noncanonical Base Pairing on RNA Folding: Structural Context and Spatial Arrangements of G·A Pairs

Noncanonical base pairs play important roles in assembling the three-dimensional structures critical to the diverse functions of RNA. These associations contribute to the looped segments that intersperse the canonical double-helical elements within folded, globular RNA molecules. They stitch together various structural elements, serve as recognition elements for other molecules, and act as sites of intrinsic stiffness or deformability. This work takes advantage of new software (DSSR) designed to streamline the analysis and annotation of RNA three-dimensional structures. The multiscale structural information gathered for individual molecules, combined with the growing number of unique, well-resolved RNA structures, makes it possible to examine the collective features deeply and to uncover previously unrecognized patterns of chain organization. Here we focus on a subset of noncanonical base pairs involving guanine and adenine and the links between their modes of association, secondary structural context, and contributions to tertiary folding. The rigorous descriptions of base-pair geometry that we employ facilitate characterization of recurrent geometric motifs and the structural settings in which these arrangements occur. Moreover, the numerical parameters hint at the natural motions of the interacting bases and the pathways likely to connect different spatial forms. We draw attention to higher-order multiplexes involving two or more G·A pairs and the roles these associations appear to play in bridging different secondary structural units. The collective data reveal pairing propensities in base organization, secondary structural context, and deformability and serve as a starting point for further multiscale investigations and/or simulations of RNA folding.

Martini bead form factors for nucleic acids and their application in the refinement of protein–nucleic acid complexes against SAXS data

The use of small-angle X-ray scattering (SAXS) in combination with molecular dynamics simulation is hampered by its heavy computational cost. The calculation of SAXS from atomic structures can be speeded up by using a coarse-grain representation of the structure. Following the work of Niebling, Björling & Westenhoff [J. Appl. Cryst. (2014), 47, 1190–1198], the Martini bead form factors for nucleic acids have been derived and then implemented, together with those previously determined for proteins, in the publicly available PLUMED library. A hybrid multi-resolution strategy has also been implemented to perform SAXS restrained simulations at atomic resolution by calculating the virtual positions of the Martini beads on the fly and using them for the calculation of SAXS. The accuracy and efficiency of the method are demonstrated by refining the structure of two protein–nucleic acid complexes. Instrumental for this result is the use of metainference, which allows the consideration and alleviation of the approximations at play in the present SAXS calculations.

Computational modeling of RNA 3D structure based on experimental data

RNA molecules are master regulators of cells. They are involved in a variety of molecular processes: they transmit genetic information, sense cellular signals and communicate responses, and even catalyze chemical reactions. As in the case of proteins, RNA function is dictated by its structure and by its ability to adopt different conformations, which in turn is encoded in the sequence. Experimental determination of high-resolution RNA structures is both laborious and difficult, and therefore the majority of known RNAs remain structurally uncharacterized. To address this problem, predictive computational methods were developed based on the accumulated knowledge of RNA structures determined so far, the physical basis of the RNA folding, and taking into account evolutionary considerations, such as conservation of functionally important motifs. However, all theoretical methods suffer from various limitations, and they are generally unable to accurately predict structures for RNA sequences longer than 100-nt residues unless aided by additional experimental data. In this article, we review experimental methods that can generate data usable by computational methods, as well as computational approaches for RNA structure prediction that can utilize data from experimental analyses. We outline methods and data types that can be potentially useful for RNA 3D structure modeling but are not commonly used by the existing software, suggesting directions for future development.

RNA3DCNN: Local and global quality assessments of RNA 3D structures using 3D deep convolutional neural networks

Quality assessment is essential for the computational prediction and design of RNA tertiary structures. To date, several knowledge-based statistical potentials have been proposed and proved to be effective in identifying native and near-native RNA structures. All these potentials are based on the inverse Boltzmann formula, while differing in the choice of the geometrical descriptor, reference state, and training dataset. Via an approach that diverges completely from the conventional statistical potentials, our work explored the power of a 3D convolutional neural network (CNN)-based approach as a quality evaluator for RNA 3D structures, which used a 3D grid representation of the structure as input without extracting features manually. The RNA structures were evaluated by examining each nucleotide, so our method can also provide local quality assessment. Two sets of training samples were built. The first one included 1 million samples generated by high-temperature molecular dynamics (MD) simulations and the second one included 1 million samples generated by Monte Carlo (MC) structure prediction. Both MD and MC procedures were performed for a non-redundant set of 414 RNAs. For two training datasets (one including only MD training samples and the other including both MD and MC training samples), we trained two neural networks, named RNA3DCNN_MD and RNA3DCNN_MDMC, respectively. The former is suitable for assessing near-native structures, while the latter is suitable for assessing structures covering large structural space. We tested the performance of our method and made comparisons with four other traditional scoring functions. On two of three test datasets, our method performed similarly to the state-of-the-art traditional scoring function, and on the third test dataset, our method was far superior to other scoring functions. Our method can be downloaded from https://github.com/lijunRNA/RNA3DCNN.

Predicting 3D structure and stability of RNA pseudoknots in monovalent and divalent ion solutions

RNA pseudoknots are a kind of minimal RNA tertiary structural motifs, and their three-dimensional (3D) structures and stability play essential roles in a variety of biological functions. Therefore, to predict 3D structures and stability of RNA pseudoknots is essential for understanding their functions. In the work, we employed our previously developed coarse-grained model with implicit salt to make extensive predictions and comprehensive analyses on the 3D structures and stability for RNA pseudoknots in monovalent/divalent ion solutions. The comparisons with available experimental data show that our model can successfully predict the 3D structures of RNA pseudoknots from their sequences, and can also make reliable predictions for the stability of RNA pseudoknots with different lengths and sequences over a wide range of monovalent/divalent ion concentrations. Furthermore, we made comprehensive analyses on the unfolding pathway for various RNA pseudoknots in ion solutions. Our analyses for extensive pseudokonts and the wide range of monovalent/divalent ion concentrations verify that the unfolding pathway of RNA pseudoknots is mainly dependent on the relative stability of unfolded intermediate states, and show that the unfolding pathway of RNA pseudoknots can be significantly modulated by their sequences and solution ion conditions.

All-atom four-body knowledge-based statistical potential to distinguish native tertiary RNA structures from nonnative folds

Scientific breakthroughs in recent decades have uncovered the capability of RNA molecules to fulfill a wide array of structural, functional, and regulatory roles in living cells, leading to a concomitantly significant increase in both the number and diversity of experimentally determined RNA three-dimensional (3D) structures. Atomic coordinates from a representative training set of solved RNA structures, displaying low sequence and structure similarity, facilitate derivation of knowledge-based energy functions. Here we develop an all-atom four-body statistical potential and evaluate its capacity to distinguish native RNA 3D structures from nonnative folds based on calculated free energy scores. Atomic four-body nearest-neighbors are objectively identified by their occurrence as tetrahedral vertices in the Delaunay tessellations of RNA structures, and rates of atomic quadruplet interactions expected by chance are obtained from a multinomial reference distribution. Our four-body energy function, referred to as RAMP (ribonucleic acids multibody potential), is subsequently derived by applying the inverted Boltzmann principle to the frequency data, yielding an energy score for each type of atomic quadruplet interaction. Several well-known benchmark datasets reveal that RAMP is comparable with, and often outperforms, existing knowledge- and physics-based energy functions. To the best of our knowledge, this is the first study detailing an RNA tertiary structure-based multibody statistical potential and its comparative evaluation.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

A nucleobase-centered coarse-grained representation for structure prediction of RNA motifs

We introduce the SPlit-and-conQueR (SPQR) model, a coarse-grained (CG) representation of RNA designed for structure prediction and refinement. In our approach, the representation of a nucleotide consists of a point particle for the phosphate group and an anisotropic particle for the nucleoside. The interactions are, in principle, knowledge-based potentials inspired by the $\mathcal {E}$SCORE function, a base-centered scoring function. However, a special treatment is given to base-pairing interactions and certain geometrical conformations which are lost in a raw knowledge-based model. This results in a representation able to describe planar canonical and non-canonical base pairs and base-phosphate interactions and to distinguish sugar puckers and glycosidic torsion conformations. The model is applied to the folding of several structures, including duplexes with internal loops of non-canonical base pairs, tetraloops, junctions and a pseudoknot. For the majority of these systems, experimental structures are correctly predicted at the level of individual contacts. We also propose a method for efficiently reintroducing atomistic detail from the CG representation.

Hierarchical Assembly of RNA Three-Dimensional Structures Based on Loop Templates

The current RNA structure prediction methods cannot keep up the pace of the rapidly increasing number of sequences and the emerging new functions of RNAs. Template-based RNA three-dimensional structure prediction methods are restricted by the limited number of known RNA structures, and traditional motif-based search for the templates does not always lead to successful results. Here we report a new template search and assembly algorithm, the hierarchical loop template-assembly method (VfoldLA). The method searches for templates for single strand loop/junctions instead of the whole motifs, which often renders no available templates, or short fragments (several nucleotides), which requires a long computational time to assemble and refine. The VfoldLA method has the advantage of accounting for local and nonlocal interloop interactions. Benchmark tests indicate that this new method can provide low-resolution predictions for RNA conformations at different levels of structural complexities. Furthermore, the VfoldLA-predicted conformations may also serve as reliable putative models for further structure prediction and refinements. VfoldLA is accessible at http://rna.physics.missouri.edu/vfoldLA .

Theory and Modeling of RNA Structure and Interactions with Metal Ions and Small Molecules

In addition to continuous rapid progress in RNA structure determination, probing, and biophysical studies, the past decade has seen remarkable advances in the development of a new generation of RNA folding theories and models. In this article, we review RNA structure prediction models and models for ion-RNA and ligand-RNA interactions. These new models are becoming increasingly important for a mechanistic understanding of RNA function and quantitative design of RNA nanotechnology. We focus on new methods for physics-based, knowledge-based, and experimental data-directed modeling for RNA structures and explore the new theories for the predictions of metal ion and ligand binding sites and metal ion-dependent RNA stabilities. The integration of these new methods with theories about the cellular environment effects in RNA folding, such as molecular crowding and cotranscriptional kinetic effects, may ultimately lead to an all-encompassing RNA folding model.

Using 3dRNA for RNA 3-D Structure Prediction and Evaluation

This unit describes how to use 3dRNA to predict RNA 3-D structures from their sequences and secondary (2-D) structures, and how to use 3dRNAscore to evaluate the predicted structures. The predicted RNA 3-D structures can be used to predict or understand their functions and can also be used to find the interactions between the RNA and other molecules. © 2017 by John Wiley & Sons, Inc.

Capturing RNA Folding Free Energy with Coarse-Grained Molecular Dynamics Simulations

We introduce a coarse-grained RNA model for molecular dynamics simulations, RACER (RnA CoarsE-gRained). RACER achieves accurate native structure prediction for a number of RNAs (average RMSD of 2.93 Å) and the sequence-specific variation of free energy is in excellent agreement with experimentally measured stabilities (R2 = 0.93). Using RACER, we identified hydrogen-bonding (or base pairing), base stacking, and electrostatic interactions as essential driving forces for RNA folding. Also, we found that separating pairing vs. stacking interactions allowed RACER to distinguish folded vs. unfolded states. In RACER, base pairing and stacking interactions each provide an approximate stability of 3-4 kcal/mol for an A-form helix. RACER was developed based on PDB structural statistics and experimental thermodynamic data. In contrast with previous work, RACER implements a novel effective vdW potential energy function, which led us to re-parameterize hydrogen bond and electrostatic potential energy functions. Further, RACER is validated and optimized using a simulated annealing protocol to generate potential energy vs. RMSD landscapes. Finally, RACER is tested using extensive equilibrium pulling simulations (0.86 ms total) on eleven RNA sequences (hairpins and duplexes).

Coarse-grained modeling of RNA 3D structure

Functional RNA molecules depend on three-dimensional (3D) structures to carry out their tasks within the cell. Understanding how these molecules interact to carry out their biological roles requires a detailed knowledge of RNA 3D structure and dynamics as well as thermodynamics, which strongly governs the folding of RNA and RNA-RNA interactions as well as a host of other interactions within the cellular environment. Experimental determination of these properties is difficult, and various computational methods have been developed to model the folding of RNA 3D structures and their interactions with other molecules. However, computational methods also have their limitations, especially when the biological effects demand computation of the dynamics beyond a few hundred nanoseconds. For the researcher confronted with such challenges, a more amenable approach is to resort to coarse-grained modeling to reduce the number of data points and computational demand to a more tractable size, while sacrificing as little critical information as possible. This review presents an introduction to the topic of coarse-grained modeling of RNA 3D structures and dynamics, covering both high- and low-resolution strategies. We discuss how physics-based approaches compare with knowledge based methods that rely on databases of information. In the course of this review, we discuss important aspects in the reasoning process behind building different models and the goals and pitfalls that can result.

Probing RNA Native Conformational Ensembles with Structural Constraints

Noncoding ribonucleic acids (RNA) play a critical role in a wide variety of cellular processes, ranging from regulating gene expression to post-translational modification and protein synthesis. Their activity is modulated by highly dynamic exchanges between three-dimensional conformational substates, which are difficult to characterize experimentally and computationally. Here, we present an innovative, entirely kinematic computational procedure to efficiently explore the native ensemble of RNA molecules. Our procedure projects degrees of freedom onto a subspace of conformation space defined by distance constraints in the tertiary structure. The dimensionality reduction enables efficient exploration of conformational space. We show that the conformational distributions obtained with our method broadly sample the conformational landscape observed in NMR experiments. Compared to normal mode analysis-based exploration, our procedure diffuses faster through the experimental ensemble while also accessing conformational substates to greater precision. Our results suggest that conformational sampling with a highly reduced but fully atomistic representation of noncoding RNA expresses key features of their dynamic nature.

SimRNA: a coarse-grained method for RNA folding simulations and 3D structure prediction

RNA molecules play fundamental roles in cellular processes. Their function and interactions with other biomolecules are dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is laborious and challenging, and therefore, the majority of known RNAs remain structurally uncharacterized. Here, we present SimRNA: a new method for computational RNA 3D structure prediction, which uses a coarse-grained representation, relies on the Monte Carlo method for sampling the conformational space, and employs a statistical potential to approximate the energy and identify conformations that correspond to biologically relevant structures. SimRNA can fold RNA molecules using only sequence information, and, on established test sequences, it recapitulates secondary structure with high accuracy, including correct prediction of pseudoknots. For modeling of complex 3D structures, it can use additional restraints, derived from experimental or computational analyses, including information about secondary structure and/or long-range contacts. SimRNA also can be used to analyze conformational landscapes and identify potential alternative structures.

Computational modeling of RNA 3D structures and interactions

RNA molecules have key functions in cellular processes beyond being carriers of protein-coding information. These functions are often dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is difficult, which has prompted the development of computational methods for structure prediction from sequence. Recent progress in 3D structure modeling of RNA and emerging approaches for predicting RNA interactions with ions, ligands and proteins have been stimulated by successes in protein 3D structure modeling.

Modeling and predicting RNA three-dimensional structures

Modeling the three-dimensional structure of RNAs is a milestone toward better understanding and prediction of nucleic acids molecular functions. Physics-based approaches and molecular dynamics simulations are not tractable on large molecules with all-atom models. To address this issue, coarse-grained models of RNA three-dimensional structures have been developed. In this chapter, we describe a graphical modeling based on the Leontis-Westhof extended base-pair classification. This representation of RNA structures enables us to identify highly conserved structural motifs with complex nucleotide interactions in structure databases. Further, we show how to take advantage of this knowledge to quickly and simply predict three-dimensional structures of large RNA molecules.

GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies

Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.

3dRNAscore: a distance and torsion angle dependent evaluation function of 3D RNA structures

Model evaluation is a necessary step for better prediction and design of 3D RNA structures. For proteins, this has been widely studied and the knowledge-based statistical potential has been proved to be one of effective ways to solve this problem. Currently, a few knowledge-based statistical potentials have also been proposed to evaluate predicted models of RNA tertiary structures. The benchmark tests showed that they can identify the native structures effectively but further improvements are needed to identify near-native structures and those with non-canonical base pairs. Here, we present a novel knowledge-based potential, 3dRNAscore, which combines distance-dependent and dihedral-dependent energies. The benchmarks on different testing datasets all show that 3dRNAscore are more efficient than existing evaluation methods in recognizing native state from a pool of near-native states of RNAs as well as in ranking near-native states of RNA models.

The role of nucleobase interactions in RNA structure and dynamics

The intricate network of interactions observed in RNA three-dimensional structures is often described in terms of a multitude of geometrical properties, including helical parameters, base pairing/stacking, hydrogen bonding and backbone conformation. We show that a simple molecular representation consisting in one oriented bead per nucleotide can account for the fundamental structural properties of RNA. In this framework, canonical Watson-Crick, non-Watson-Crick base-pairing and base-stacking interactions can be unambiguously identified within a well-defined interaction shell. We validate this representation by performing two independent, complementary tests. First, we use it to construct a sequence-independent, knowledge-based scoring function for RNA structural prediction, which compares favorably to fully atomistic, state-of-the-art techniques. Second, we define a metric to measure deviation between RNA structures that directly reports on the differences in the base–base interaction network. The effectiveness of this metric is tested with respect to the ability to discriminate between structurally and kinetically distant RNA conformations, performing better compared to standard techniques. Taken together, our results suggest that this minimalist, nucleobase-centric representation captures the main interactions that are relevant for describing RNA structure and dynamics.

Protein-RNA complexes and efficient automatic docking: expanding RosettaDock possibilities

Protein-RNA complexes provide a wide range of essential functions in the cell. Their atomic experimental structure solving, despite essential to the understanding of these functions, is often difficult and expensive. Docking approaches that have been developed for proteins are often challenging to adapt for RNA because of its inherent flexibility and the structural data available being relatively scarce. In this study we adapted the RosettaDock protocol for protein-RNA complexes both at the nucleotide and atomic levels. Using a genetic algorithm-based strategy, and a non-redundant protein-RNA dataset, we derived a RosettaDock scoring scheme able not only to discriminate but also score efficiently docking decoys. The approach proved to be both efficient and robust for generating and identifying suitable structures when applied to two protein-RNA docking benchmarks in both bound and unbound settings. It also compares well to existing strategies. This is the first approach that currently offers a multi-level optimized scoring approach integrated in a full docking suite, leading the way to adaptive fully flexible strategies.

A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions

A unified coarse-grained model of three major classes of biological molecules—proteins, nucleic acids, and polysaccharides—has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site–site interactions as mean-field dipole–dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo’s cluster-cumulant series leads to the appearance of mean-field dipole–dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and β-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented.

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The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.